الفهرس 
SLIP-LINE ANALYSIS OF GRANULAR MATERIALS USING OBLIQUE COORDINATE SYSTEMOnly 14 pages are availabe for public view
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Abstract
A theoretical study of the mechanical behavior of dilatant granular
materials is presented. In this work, the double sliding model proposed by
Mehrabadi and Cowin (1978) which based on Mohr-Coulomd criterion, for the
post-failure behavior of dilatant granular materials is derived by an
alternative way, namely, introducing an oblique coordinate system which
could account to some extent and yields considerable mathematical
simplicity comparing with using othogonal coordinate system. Three
different boundary value problems employing the constitutive relations of
the dilatant sliding deformation model are considered.
Coulomb’s model of failure in a soil proposes slip on planes of
maximum stress obliquity, and even after two hundred years this model is
still a fundamental tool for geotechnical engineers. Confidence in
Coulomb’s concept has been continually revived by the discovery of thin
rupture layers in investigations of landslides and foundation failures. As
a result from Mohr-Coulomb criterion, a straight slip plane is predicted
at failure with certain inclination. However, the theory of plasticity and
the introduction of radiography into soil mechanics research had led to
new conflecting interpretations; in fact, the generation of strain
discontinuities in soils is complex and occurs in a variety of ways which
indicate that the slip directions are away from that given by Coulomb’s
solution, which is the aim of the rest of this work to clarify this point.
Based on a microscopical approach, a stress-dilatacy equation for
two dimensional deformation of granular materials is derived which
explains in a Simple and convincing manner the physically observed
phenomenon of initial densification and subsequent dilatancy that
accompany the shearing of these materials. This approach complements the work of Mehrabadi and Cowin who focused attention on the phenomenon of
dilatancy of a very densely packed sample. Guided by the SMP concept
(Matsouka,1974), a proposed three dimensional dilatancy equation is also
derived. It is found that, this approach which is based on the sliding
mechanism between particle groups of the granular materials seems to
provide an alternative way towards the objective of better understanding
the mechanical behavior of granular materials.
A micromechanically based constitutive model of granular materials
is formulated in which both contributions due to fabric change’s and to
slippages among particles are incorporated depending on realistic slip
direction as observed from many experiments. In the context of this model
an expression is obtained for the directions of shear bands in which
bifurcation of the deformation is possible. The agreements between the
model prediction and the experimental observations are found to be
satisfactory.
Finally, an analytical equation and a numerical solution for
predicting the ultimate bearing capacity of a surface smooth strip footing
under plane strain condition is obtained taking into account the suggested
slip direction. The predicted bearing capacity by the two approaches lead
to a reasonable result which is found to agree with other published
experimental data.